It's at least plausible: a length extension will cause a crop to end up on the sensor/film and thus will cause a loss of light. How much effect an extension has depends on effective diameter and position of the last optical element. Also an extension tube will require a different focus setting. Again, the amount of difference will depend on effective diameter and position of the last optical element. If you are unlucky, the focus range after extension is not generally useful. It will usually work for the purpose of closeup photography. However, how good the results are depends on the optical recipe of the lens since things like flat field correction and chromatical aberration compensation are done with a fixed sensor plane in mind.
For mirror lenses, the strongest optical element may be the mirror which does not need chromatical aberration compensation. At least that may be an advantage.
So the claim is plausible. Whether it is true would require someone with personal experience to corroborate.